The fundamental interactions of nature are governed by symmetries. The observable properties of physical systems can support different manifestations of these symmetries. Phase transitions often characterize the transition of a physical system from one symmetry status to another. These transitions themselves encode important information about the relevant degrees of freedom of physical systems.

We study the symmetries of physical systems as they occur in relativistic particle physics or many-body physics. Of particular interest are chiral symmetries, local gauge symmetries, and supersymmetry. Phase transitions that correspond to spontaneous or dynamical breaking of such symmetries are intimately related to profound questions such as the generation of mass in the universe and many further properties of the variety of particles in nature.